I’m tinkering with a longer post that considers the different directions or models I know about for what math is and what teaching it means, but in the mean time, Michael Lomuscio’s comment on Dan Meyer’s blog has done a lot of the spade work. He covers some ground that reminded me of Riley’s discussions of fluency, but to me the best snippet is this one:
A problem’s worth should be based on the level of creativity it demands from the student. Does the problem give them room to engage in the creative process of mathematics? If mathematics IS a creative process, then no math can be accomplished in the absence of creativity or creative potential. Are we handing students a blank canvas that they can express themselves on? Can they be proud of their work of art? Or, are we handing them a paint by numbers picture instantly killing any chance for creativity and robbing them of ownership and pride that they could, and should, feel in their work?